The fact that the GPL uses copyright is just an implementation detail.

In actual practice, it does the opposite of normal copyright. Copyright is usually used to restrict access to some work. A public domain work can be accessed to anyone, but, as it evolves, future contributors can restrict access to it. A GPL work remains accessible to everyone in perpetuity, not just from a legal standpoint but also from a practical standpoint (no need to reverse engineer or disassemble). Not only are you allowed to use the work, but also nobody is allowed to stop you from using it in any form. It really is on the opposite side of the spectrum from normal copyright (we can imagine public domain to be the midpoint).

In the FSF's perfect world, the GPL would not be necessary. Instead, you would be able to access and modify all your software without restriction. The GPL is just a clever way of creating and enforcing such a world without changing existing legislature.

Also, "intellectual property" is an unfortunate and rather loaded term. For one, it covers several distinct concepts like copyright, patents and trademarks which all behave differently and have different ramifications. Secondly, it presents a false parallel to real property. Whatever you think of Stallman's ideology, you have to admit he is a good writer (certainly infinitely better than I am) and very clear; here is his case against the term "intellectual property": http://www.gnu.org/philosophy/not-ipr.html

A final note: while the general software community is divided on patents and copyright, I don't think most people are against trademark law. If anything, trademark law is about fraud--you're not allowed to lie to customers about being affiliated with a known, existing brand. I suspect most people arguing for copyright and patent reform are fundamentally fine with trademark law as is, or want minor changes to it at most.

Normal copyright gives an author a "bundle of rights" that they may license how they want or declare to be in the public domain. Even if you classify the GPL as "copyleft, not copyright" or "legal judo," I don't think it works opposite of the way that normal copyright does. In a world where everything was public domain it would still be possible to circumvent GPL's source code distribution provisions.

There is one part of copyright that might run counter to the GPL, however, and that is the right of an author to reclaim copyright after 35 years. If the right applies (i.e. not a work legally classed as work for hire) it cannot be revoked, even by the author, until the 35 year term is nearly over. This right is generally a good thing, but might be a bit messy or disruptive if someone who wrote old UNIX IP decides to try to reclaim their work.

Unfortunate or not, intellectual property is a term of art at this point. However, connotation can differ from denotation, and it often does in law.